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Delay time in sequential detection of change

Alexander Aue and Lajos Horvath

Statistics & Probability Letters, 2004, vol. 67, issue 3, 221-231

Abstract: We consider a sequential test procedure which detects possible changes in the mean of observations satisfying a weak invariance principle. Our test statistic is based on weighted CUSUMs of the underlying random variables. In this paper, we study the asymptotic behaviour of the delay time if a change has occurred in the sample after a training period of size m in which the observations stay in control. It turns out that in this situation the limiting distribution of the delay time for m-->[infinity] is normal under a suitable standardization provided the change appeared sufficiently soon after m.

Keywords: Change-point; estimation; Sequential; procedure; Wiener; process; Partial; sums; Invariance; CUSUM; Drift (search for similar items in EconPapers)
Date: 2004
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